Real Madrid will face defending champions Barcelona in the semifinals of the Copa del Rey while Real Betis will play Valencia in the other semifinal.
The draw made on Friday means there will be back-to-back Clasicos, with the second leg due to take place in the last week of February, before Madrid host Barca in La Liga on March 2.
The first leg will be played at the Camp Nou next week before a return at the Santiago Bernabeu.
Real Madrid's club director Emilio Butragueno said after the draw: "Madrid against Barcelona is one of the best matches that can be seen all over the world today. It will be a great knock-out match."
Two Clasico games in a week will crank up the pressure on both teams at the end of the month but Real also have a testing schedule around the first leg.